Research in Algebra
Including number theory, algebraic geometry, and combinatorics
We have large groups of researchers active in number theory and algebraic geometry, as well as many individuals who work in other areas of algebra: groups, noncommutative rings, Lie algebras and Lie super-algebras, representation theory, combinatorics, game theory, and coding. A number of members of the algebra group belong to the Research Training Group in Representation Theory, Geometry and Combinatorics, which runs activities and supports grad students and postdocs in its areas of interest.
Courses
Undergraduate upper division courses
Math 110 (and honors version, Math H110). Linear algebra.
Math 113 (and honors version, Math H113). Introduction to abstract algebra.
Math 114. Second course in abstract algebra. (Instructor's choice; usually Galois Theory)
Math 115. Introduction to number theory.
Math 116. Cryptography.
Math 143. Elementary algebraic geometry.
Math 172. Combinatorics.
The Mathematics Department also offers, at the undergraduate level,
courses which may include algebraic topics along with others: Problem
Solving (H90), Experimental Courses (191), a Special Topics course
(195), and several courses of directed and independent individual and
group work (196-199).
Graduate courses
Math 245A. General theory of algebraic structures.
Math 249. Algebraic combinatorics.
Math 250A. Groups, rings and fields.
Math 250B. Multilinear algebra and further topics.
Math 251. Ring theory.
Math 252. Representation theory.
Math 253. Homological algebra.
Math 254A-254B. Number theory.
Math 255. Algebraic curves.
Math 256A-256B. Algebraic geometry.
Math 257. Group theory.
Seminars
2008-2009
Math 290. Seminar - Commutative algebra and algebraic geometry, David Eisenbud
Math 290. Seminar - Number theory, Kenneth Ribet
Spring 2009
Math 274. Topics in Algebra - Tropical geometry, Bernd Sturmfels
Math 274. Topics in Algebra - Infinitesimal geometry, Mariusz Wodzicki
Fall 2008
Math 290. Seminar - Algebraic geometry, David Eisenbud and Daniel Erman
Math 290. Seminar - Discrete mathematics, Bernd Sturmfels
Math 290. Seminar - Representation theory, geometry and combinatorics, Mark Haiman and Nicolai Reshetikhin
Math 290. Seminar - Student arithmetic geometry seminar, Martin Olsson
Student Seminar. Student algebraic and arithmetic geometry seminar, David Brown, Daniel Erman and Anthony Varilly
2007-2008
Math 270. Hot Topics - Derived algebraic geometry and topology, Peter Teichner
Math 290. Seminar - Commutative algebra and algebraic geometry, David Eisenbud
Math 290. Seminar - Representation theory, geometry and combinatorics, Mark Haiman and Nicolai Reshetikhin
Spring 2008
Math 274. Topics in Algebra - Real p-adic analysis, Robert Coleman
Fall 2007
Math 274. Topics in Algebra - Locally finite lie algebras and their representations with a view toward open problems, Ivan Penkov
Math 290. Seminar - Student representation theory, geometry and combinatorics, Vera Serganova and Peter Tingley
Math 290. Seminar - Number theory, Kenneth Ribet
Math 290. Seminar - Perverse sheaves, Joel Kamnitzer and Xinwen Zhu
Senate Faculty
| Name | Title | Research Interests |
|---|---|---|
| George M. Bergman | Professor Emeritus, Professor of the Graduate School | Associative rings, Universal algebra and category theory, Counterexamples |
| Richard E. Borcherds | Professor | Lie algebras, Vertex algebras, Automorphic forms |
| Robert F. Coleman | Professor | Arithmetic geometry |
| David Eisenbud | Professor | Algebraic geometry, Commutative algebra, Computation |
| Edward Frenkel | Professor | Representation theory, Integrable systems, Mathematical physics |
| Mark D. Haiman | Professor | Algebra, combinatorics, and algebraic geometry |
| Robin C. Hartshorne | Professor Emeritus | Algebraic geometry, History of geometry |
| Tsit-Yuen Lam | Professor Emeritus, Professor of the Graduate School | Algebra |
| Hendrik W. Lenstra, Jr. | Professor Emeritus | Algebraic number theory, Algorithms |
| Andrew P. Ogg | Professor Emeritus | Number theory, Elliptic curves, Modular forms |
| Arthur E. Ogus | Professor | Algebraic geometry |
| Martin Olsson | Professor | Algebraic and arithmetic geometry |
| Nicolai Reshetikhin | Professor | Mathematical physics, Low-dimensional topology, Representation theory |
| John L. Rhodes | Professor Emeritus | Algebra, Semigroups, Automata |
| Kenneth A. Ribet | Professor | Algebraic number theory, Algebraic Geometry |
| Ichiro Satake | Professor Emeritus | Symmetric spaces, Automorphic functions |
| Vera Serganova | Professor | Super-representation theory |
| Bernd Sturmfels | Professor | Combinatorics, Computational algebraic geometry |
| Constantin Teleman | Professor | Lie groups, Algebraic geometry, Topology, Quantum field theory |
| Paul A. Vojta | Professor | Diophantine approximation, Nevanlinna theory-especially as related to diophantine approximation, Arakelov theory |
| Lauren Williams | Assistant Professor | Combinatorics, and connections to representation theory, geometry, and statistical physics |
| Mariusz Wodzicki | Professor | Non-commutative and algebraic geometry, Analysis, K-theory |
| Xinyi Yuan | Assistant Professor | Number theory |
Visiting Faculty
| Name | Title | Research Interests |
|---|---|---|
| Federico Ardila | Visiting Scholar | Algebraic, geometric, and topological combinatorics; tropical geometry |
| Mats Boij | Visiting Scholar | Commutative algebra, minimal free resolutions |
| Mei-Chu Chang | Visiting Scholar | Combinatorial number theory |
| Joan Elias | Visiting Scholar | Commutative algebra, analytic classification of Artin algebras |
| Max Glick | Visiting Assistant Professor | Algebraic combinatorics, cluster algebras |
| Hamid Rahkooy | Visiting Scholar | Computational algebraic geometry, Gröbner bases, use of (sub)resultants in Gröbner basis computation |
| Helge Ruddat | Visitor | Algebraic geometry and mirror symmetry; Calabi-Yau varieties |
| Zvezdelina Stankova | Visiting Professor & Director, Berkeley Math Circle | Algebraic geometry, representation theory, combinatorics, Olympiad problem solving, Berkeley Math Circle |
| Friedrich Wagemann | Visiting Scholar | Homological algebra, integration of Courant algebras |
Postdocs
| Name | Title | Research Interests |
|---|---|---|
| Florian Block | Humboldt Postdoctoral Fellow | Algebraic combinatorics, tropical geometry |
| James Freitag | NSF Postdoctoral Fellow | Model theory, differential algebra, algebraic geometry |
| Noah Giansiracusa | RTG Postdoctoral Fellow | Algebraic geometry, moduli spaces |
| Nathan Ilten | Morrey Assistant Professor | Toric geometry and deformation theory |
| Alice Medvedev | FRG Postdoctoral Fellow | Model Theory, Algebraic Dynamics |
| Steven Sam | MILLER FELLOW | Commutative algebra, representation theory, algebraic combinatorics |
| Kelli Talaska | NSF Postdoctoral Fellow | Centered in algebraic combinatorics, with a special focus on connections between matrix algebra and enumeration in planar networks. |
Faculty with Related Research Interests
| Name | Title | Research Interests |
|---|---|---|
| Denis Auroux | Professor | Symplectic topology and mirror symmetry |
| Elwyn R. Berlekamp | Professor Emeritus | Combinatorial game theory, Algebraic coding theory, Electrical engineering, Computer science |
| Olga Holtz | Professor | Numerical analysis, matrix theory, algebra and combinatorics, computational complexity |
| Ralph McKenzie | Professor Emeritus | General algebra, Logic |
| Calvin C. Moore | Professor Emeritus | Representations and actions of topological groups, Operator algebras |
| Lior Pachter | Professor | Mathematical and computational biology |
| Marc A. Rieffel | Professor | Non-commutative harmonic analysis, Operator algebras, Quantum geometry |
| Thomas Scanlon | Professor | Model theory and applications to number theory |
Graduate Students
| Name | Dissertation Supervisor |
|---|---|
| Piotr Achinger | Arthur E. Ogus |
| Natth Bejraburnin | Lior Pachter |
| David Berlekamp | David Eisenbud |
| Shuchao Bi | Olga Holtz |
| Adam L. Boocher | David Eisenbud |
| Sarah B. Brodsky | |
| Anastasia Chavez | |
| Harrison Chen | |
| Andrew J. Critch | Bernd Sturmfels |
| Michael W. Daub | Kenneth A. Ribet |
| Daniel Halpern-Leistner | Constantin Teleman |
| Katrina Honigs | Martin Olsson |
| Yuhao Huang | Martin Olsson |
| Theodore Johnson-Freyd | Nicolai Reshetikhin |
| Alex Kruckman | Thomas Scanlon |
| Lasse Peter Mannisto | Martin Olsson |
| Lilit Martirosyan | Vera Serganova |
| James McIvor | |
| George W. Melvin | Constantin Teleman |
| Maria Monks | Mark Haiman |
| Khoa Nguyen | Paul A. Vojta |
| Andrew Niles | Martin Olsson |
| Jae-Young Park | Martin Olsson |
| Eric C. Peterson | Constantin Teleman |
| Zvi Rosen | |
| Alexander Shapiro | |
| Pablo Solis | Constantin Teleman |
| Matthew Tucker-Simmons | Marc A. Rieffel, Nicolai Reshetikhin |
| Thanh Quang Vu | |
| Harold M. Williams | Nicolai Reshetikhin |
| Hwajong Yoo | Kenneth A. Ribet |
Recent Ph.D.s
| Name | Dissertation Title | Dissertation Supervisor | Year |
|---|---|---|---|
| Morgan Brown | Cox Rings and Partial Amplitude | David Eisenbud | 2012 |
| Melody Chan | Tropical curves and metric graphs | Bernd Sturmfels | 2012 |
| Chul Hee Lee | Algebraic Structures in Modularq-hypergeometric Series | Richard E. Borcherds | 2012 |
| Edgard Rincon | Tropical Linear Spaces andApplications | Olga Holtz, Bernd Sturmfels | 2012 |
| Jeffrey Doker | Geometry of Generalized Permutohedra | Federico Ardila at SFSU, Matthias Beck at SFSU, Lior Pachter, Bernd Sturmfels, Lauren Williams | 2011 |
| Anton Igorevich Geraschenko | Toric Stacks | Vera Serganova | 2011 |
| An Huang | On Conformal Field Theory and Number Theory | Richard Borcherds | 2011 |
| Claudiu Cristian Raicu | Secant Varieties of Segre-Veronese Varieties | David Eisenbud | 2011 |
| William Slofstra | Strong Macdonald Theory and theBrylinski Filtration for Affine Lie Algebras | Constantin Teleman | 2011 |
| Cynthia Leslie Vinzant | Real Algebraic Geometry in Convex Optimization | Bernd Sturmfels | 2011 |
| David Michael Brown | Rigid Colomology of Algebraic Stacks | Kenneth A Ribet | 2010 |
| Dustin Alexander Cartwright | Applications of non-linear algebra to biology | Bernd Sturmfels | 2010 |
| Li-Chung Chen | Skew-Linked Partitions and a Representation-Theoretic Model for K-Schur | Mark Haiman | 2010 |
| Maria Angelica Cueto | Tropical implicitization | Bernd Sturmfels | 2010 |
| Daniel Erman | Applications and Extensions of Boij-Soderberg Theory | David Eisenbud | 2010 |
| Alexander Fink | Matroid Polytope Subdivisions and Valuations | Bernd Sturmfels | 2010 |
| Manuel Lionel Reyes | One-Sided Prime Ideals in Noncommutative Algebra | Tsit-Yuen Lam | 2010 |
| Matthew Satriano | Stacky Resolutions of Singular Schemes | Martin Olsson | 2010 |
| Shenghao Sun | On I-Adic Cohomology of Artin Stacks: L-Functions, Weights and the Decomposition Theorem | Martin Olsson | 2010 |
| Bianca Viray | The Algebraic Brauer-Marnin Obstruction on Chatelet Surfaces, Degree 4 del Pezzo Surfaces, and Enriques Surfaces | Bjorn Poonen | 2010 |
| Jonah Blasiak | Cyclage, catabolism, and the affine Hecke algebra | Mark Haiman | 2009 |
| Ishai Dan-Cohen | Moduli of nondegenerate unipotent representations | Martin Olsson, Arthur Ogus | 2009 |
| Seth Dutter | Logarithmic Jet Spaces and Intersection Multiplicities | Paul Vojta | 2009 |
| Sevak Mkrtchyan | Scaling limits of random skew plane partitions | Nicolai Reshetikhin | 2009 |
| Brian Rothbach | Borerl orbits of x2 = ) in gln | Mark Haiman | 2009 |
| Arun Sharma | The Structure of 3-free Permutations | Mark Haiman, Ron Graham | 2009 |
| Anthony Varilly-Alvarado | Arithmetic of del Pezzo surfaces of degree 1 | Bjorn Poonen | 2009 |
| Xiwen Zhu | Gerbal representations of double loop groups | Edward Frenkel | 2009 |
| Jameel Al-Aidroos | Perfect Pairings in the Tautologicl Rings of the Moduli Spcaes of Stable Curves | Graber, David Eisenbud | 2008 |
| Jennifer Danae Berg | On the center of the Lie superalgebra q(n)(2) | Vera Serganova | 2008 |
| Elizabeth Dan-Cohen | Structure of root-reductive Lie algebras | Vera Serganova, Joseph A. Wolf | 2008 |
| Jesse Fern | Calculations of Quantum Error Correction and Fault Tolerance Thresholds | Vera Serganova, Birgitta Whaley | 2008 |
| David Stephen Freeman | Constructing Abelian Varieties for Pairing-Based Cryptography | Kenneth Ribit, Edward Schaeffer | 2008 |
| Peter McKinley Huggins | Polytopes in Computational Biology | Lior Pachter, Bernd Sturmfels | 2008 |
| Dimitar Petkov Jetchev | CM Points, Selmer groups, component groups and Euler Systems | Kenneth Ribit | 2008 |
| Peter William Tingley | Some results on the crystal commutor and affine sl(n) crystals | Nicolai Reshetikhin | 2008 |
| David James Zywina | The large sieve and Galois representations | Bjorn Poonen | 2008 |
